The LC3 (LC2?) came with a rear diff lock, all others only have a centre diff lock as standard and rely on ATRAC-II (Toyota's traction control system) to manage wheel slip. Gary bought a OEM rear locker and one of these days, should do a write up (hint hint nudge nudge)

The diff lock we have simply locks the front and rear dive shafts together, regardless of if you are in H or L.

Assume you are driving and your front left tyre looses traction. Atrac will sense (using the ABS sensors) that the front wheel is not rotating at the same speed as the right.
By it's very nature, a diff "sends" more torque to the wheel with the least grip. This would mean your left tyre gets all the drive and the right, which still has traction, gets none.
Atrac will then clamp the brake for a few ms which then allows the diff to send some of the torque to the right wheel because the left wheel is not free to spin any more. Once released, the whole lot starts over again as the car actually has no way to tell when the left wheel has found solid ground again. For this reason it is pulsed on and off until there is no difference in rotation.

Now, onto why you need a CD locker (Centre Diff).
Because of the above, you would actually loose drive to all wheels. as the CD "sends" the torque to the front and the front diff to the left wheel. You've lost it all.
The centre lock stops this by locking front to back. That way, torque is split regardless of amounts of traction on the front axle or rear axle. Should you loose drive to the front or back, then the brakes on each axle will try sort out their now independent lives.

A classic way to see its use was with the snow. (The experiment works now as well).
Along one of the local country lanes here, there is a nice embankment up the side of one. If you approach it square on, you get to drive up until the front loose grip on the grass / snow. With an open CD (unlocked) you loose everything pretty much as soon as your front wheels are on the grass and you pointing up. They are both slipping, ATRAC is trying it's best to help out but is failing. Because the front has lost everything, the CD will not be "sending" and torque to the rear.
Lock the CD and try the exercise again and you make it up. The reason being, the CD is locked, drive is lost on the front but the rear wheels are still on tar and are now pushing you up.

All of this has nothing to do with your T-Case being in H/L.
When to lock the CD? When on snow if you slipping or just 'cause. Some folks turn it on if they approaching a puddle (Always bloody on then ) or if you loose traction to either the front or the back. You can, according to the book, turn it on while moving up to speeds of 50mph. I've done this and only on one occasion felt a slight thud (I was driving on a bend) when it engaged.
If you have it locked when on normal tar, you'll get drive train wind-up. When you go around a corner, the front wheels track differently to the rear. This difference is normally absorbed by the diffs (all 3 of them) Lock any one of them and you will hear the tyres scrubbing when cornering and get a heavy steering wheel. I turned it on by accident and tried to do a U-Turn. The steering wheel pulled out my hand because of it.
Absolute worst case: You'll snap something (but that's apparently not likely)

The interesting thing with the ATRAC was the guys suggestion that it works better when you are going slowly. If you have 3 lockers, you could just boot it and fight your way out. With ATRAC, the computer needs time to work out what to do. Giving it some wellie seems to worsen the situation. Makes sense really.

If you wanted to lock all 4 wheels together, you would have to lock all three diffs. Don't know anyone here with a 120 with 3 lockers on but a lot of the chaps with 80s, some 90s and some 100s have the 3 lockers. Once all locked, you could drive with 3 wheels in the air without any fuss. We would still have some fuss as the ATRAC tries to help us out.

If you had a LC3 you could lock front to back (CD) as well as rear together.

Like everything on the 120, it's a cost thing. Chelsea tractor market would not use it so they would rather rely on some electricery than fit the diff locks.
I think the Aussies can get them on higher rated options.

I remember reading about that. hey have a "diff club" now don't they?
Are they Toyota lockers that break or was it over zealous ATRAC / VSC which caused the failure.
I seem to remember something about not disabling VSC (by locking CD) which then got all excited and camped a wheel with lots of energy in it (spinning moer se fast ) which then caused massive failure.

err - no - kinda put that on the back-burner for now. I am rapidly running out of time - want to get that rear door, need to build the packing system, got the roof rack on it's way - that needs fitting and modding for GPS units, antenna, etc. - I know not a big job but it'll take time. Then I still want to order the suspension and get that fitted, and the BOAB data-logger to receive and fit ... and only 11 weekends left, of which I'll be working 4 of them at least ...

I had to sort the garage out this weekend, along with SWMBOs studio, so that was that gone But I have a bit more space to use now

Jeez - can you imagine the chaos - diff oil everywhere and trucks sliding on those decks - yee-ha!!

I'd be very tempted to have a go if I could suss out what to do re the ECU and loom ... the switch is easy, the locker not so (I'm not sure that the housing doesn't need work) but the electrickery in-between is a puzzle ...